Effect of high-energy neutron source on predicting the proton beam current in the ADS design

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Effect of high-energy neutron source on predicting the proton beam current in the ADS design. The results show that high-energy neutrons with En > 20 MeV are of small fraction (2.6%) in the neutron source, but their contribution to the source efficiency is about 23% for the large scale ADS. Based on this, a neutron source efficiency correction factor is proposed. Tests show that the new correction method works well in the ADS calculation. This method can effectively improve the accuracy of the prediction of the proton beam current.
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Nuclear Engineering and Technology
journal homepage: www.elsevier.com/locate/net
Original Article
Effect of high-energy neutron source on predicting the proton beam
current in the ADS design
Youqi Zheng*, Xunzhao Li, Hongchun Wu
School of Nuclear Science and Technology, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, China
a r t i c l e
i n f o
a b s t r a c t
Article history:
The accelerator-driven subcritical system (ADS) is driven by a neutron source from spallation reactions
Received 8 June 2017
Received in revised form
9 August 2017
Accepted 20 August 2017
Available online 16 October 2017
introduced by the injected proton beam. Part of the neutron source has energy as high as a few hundred
MeV to a few GeV. The effects of high-energy source neutrons (En > 20 MeV) are usually approximated by
energy cut-off treatment in practical core calculations, which can overestimate the predicted proton
beam current in the ADS design. This article intends to quantize this effect and propose a way to solve
this problem. To evaluate the effects of high-energy neutrons in the subcritical core, two models are
Keywords:
Accelerator-driven System
Correction Method
High-energy Neutron Source
established aiming to cover the features of current experimental facilities and industrial-scale ADS in the
future. The results show that high-energy neutrons with En > 20 MeV are of small fraction (2.6%) in the
neutron source, but their contribution to the source efciency is about 23% for the large scale ADS. Based
on this, a neutron source efciency correction factor is proposed. Tests show that the new correction
Neutron Source Efciency
method works well in the ADS calculation. This method can effectively improve the accuracy of the
Proton Beam Current
prediction of the proton beam current.
© 2017 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the
1. Introduction
The other problem is caused by the incomplete nuclear data in
the high-energy range. In MCNPX, some physical models are
The accelerator-driven system (ADS) is recognized as a candi-
applied to obtain data in the high-energy range. However, for
date for advanced clean and safe nuclear systems [1]. It will be used
many other codes used for core calculation, only the evaluated
in the future to effectively transmute the minor actinides. Because
data can be used. Owing to the difculty of evaluating nuclear data
of the existence of a high-energy neutron source, the neutronics
in the very high-energy range, the data in current libraries are not
feature of ADS is distinctly different from those of other traditional
complete. For example, in the high-energy nuclear library JENDL-
nuclear reactors. More parameters such as the neutron source ef-
HE-2004, there are only 66 nuclides. In the new, updated version,
ciency and the proton beam current are required in the ADS
i.e., JENDL-HE-2007, 41 more nuclides have been added; however,
simulation [2].
this is not enough to fulll the requirements of transmutation
To obtain the required proton beam current for the ADS design,
analysis.
the neutronics calculation should be done rst. Carrying out a
Therefore, in practice till now, ADS calculation has been
complete calculation from spallation to neutron transport at low
commonly divided into two steps [6,7]. In the rst step, the high-
energy is the ideal way to do this; however, two difculties are
energy Monte Carlo particle transport codes, such as MCNPX,
encountered.
NMTC/JAERI97 [8], and FLUKA [9], are used to simulate the spall-
One problem is that the computational cost is heavy. Among the
ation reactions and obtain the neutron source. In the second step,
neutronics calculation tools, the MCNPX code [3] is an ideal choice
either Monte Carlo codes [10e12] or deterministic transport codes
for complete modeling and simulation. It is a combination of the
[13e15] are used to calculate the core performance. While the
high-energy physics code LAHET [4] and the Monte Carlo particle
calculation is split into two steps, special methods should be used
transport code MCNP [5]. However, huge computational memory
to dene the neutron source coming from the spallation reactions.
and a great deal of time are required.
Till now, there have been four different denitions of the neutron
source, including target neutron leakage source, energy cut-off
* Corresponding author.
E-mail address: yqzheng@mail.xjtu.edu.cn (Y. Zheng).
source, ssion source, and primary neutron source. The rst two
denitions are widely accepted. The target neutron leakage source
1738-5733/© 2017 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/
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Y. Zheng et al. / Nuclear Engineering and Technology 49 (2017) 1600e1609
1601
uses neutrons that leak out radially from the target as source
source and the subcriticality. For any given values of subcriticality
neutrons. So, high-energy neutrons are considered explicitly in the
and external neutron source, a larger source efciency means
denition of the source. The energy cut-off neutron source uses
neutrons that fall below a certain cut-off energy (usually 20 MeV).
To obtain the cut-off neutron source, combined target and core
calculation are required. The ssion source consists of the rst
more ssion power produced in the subcritical core [2,19].
4* ¼ k1f  1 $Ff
(1)
generation of ssion neutrons in the subcritical core. The primary
neutron source is the number of neutrons that are created directly
from proton-induced spallation.
Using the target neutron leakage source is easier and more ac-
curate, but a new cross-section library considering high-energy
reactions is necessary. Compared with using the target neutron
leakage source, using the energy cut-off neutron source is more
exible and can t the traditional transport codes. However, the
where, keff is the effective multiplication factor, Ffis the total
production of neutrons by ssion, and Sis the total production of
source neutrons by the incident proton source.
The total power produced by ssion in the core can be expressed
as the product of the total number of ssion events and the average
available energy released in one instance of ssion, according to the
following relation:
distribution of the neutron source is sensitive to changes of the
subcritical core [16]. Therefore, this approach is also expensive in
practical analysis.
.
Pf ¼ Ffv,Ef
(2)
A more efcient method to proceed is to combine these two
approaches, i.e., using the target neutron leakage source but cutting
off the source at a certain energy level to t the following transport
calculation in the core. The main drawback is that during the cut-
ting off of the source, high-energy neutrons emitted from the
spallation reactions are ignored.
Seltborg and Jacqmin [17], based on MUSE-4 experiment in the
framework of the MUSE experiments (multiplication avec source
where, v is the average number of ssion neutrons per ssion
event and Ef is the average energy released per ssion.
Substituting Eq. (1) into Eq. (2), the total production of neutrons
by the incident proton can be written as:
!,
S¼ Pf v 1  1 Ef 4* (3)
eff
externe) at CEA, found that the small fraction of high-energy neu-
trons (En > 20 MeV) contributes signicantly to the neutron source
efciency and to the total number of ssion neutrons produced in
The relationship between the total number of protons hSpi and
the total production of neutrons Sis:
the core. In order to take the effect of high-energy neutrons into
account, correction factors of proton source efciency, number of
S¼ z$Sp
(4)
source neutrons per proton, and neutron source efciency were
analyzed by Fokau et al. [18].
Based on previous studies, this article quantitatively evaluates
the effects of energy cut-off on the neutronics calculation and ex-
where, z is the neutron yield from one instance of proton injection
(spallation neutron yield).
Substituting Eq. (4) into Eq. (3)
tends the conclusion to both the small-size experimental ADS used
nowadays and the large scale ADS (ADS burner for nuclear waste
transmutation) with GeV protons that will be used in the future.
The idea of using a correction method is also extended. The
sensitivity of the correction factor is analyzed considering the
Sp ¼ Pf v 1  1!,zEf 4* (5)
eff
Hence, the proton beam current required for certain core power
depletion of the ADS reactor core.
can be obtained by:
In this article, two models are established. For each model, the
neutron source is decomposed into several energy intervals, and
three levels of subcriticality are considered. The values and the
variation tendencies of the correction factor are discussed while
Ip ¼ ePf v
!,
1  1 zEf 4*
eff
(6)
considering the depletion.
Besides this, the effectiveness of the correction factor is tested at
three different subcritical levels. Overestimation of required proton
and neutron sources in different ADSs is quantied, and the benet
of using the correction method is shown in the numerical results.
This article is organized as follows. Section 2 provides a detailed
description of the calculation methodology and models. Section 3
shows the effects of high-energy neutrons and the application of
the correction factor in the ADS calculations. The nal section
provides the conclusions.
where, e is the charge of proton.
For a given fuel composition and certain core power, the higher
the neutron source efciency, the smaller the proton beam current
that is required. The values of z and 4*essentially depend on the
source neutrons [20]. Therefore, the key problem is how to evaluate
the neutron source efciency in practice. This evaluation is sensi-
tive to the cut-off energy if the neutronics calculation is split into
two steps.
To analyze the energy cut-off effect [17,21], the neutron source
efciency 4* is decomposed into several energy intervals, as in
Eq. (7):
2. Materials and methods
2.1. Computational methods for ADS
4i ¼
!
1  1 $hFfii
eff i
(7)
The source efciency, denoted as 4* in Eq. (1), represents the
where, i is the index of the energy range.
average importance of the external neutron source. It relates the
The neutron source efciency 4*ðcÞ, with different levels of cut-
total ssion neutron production Ffto the external neutron
off energy, can be obtained as: